The present invention relates to a computer-aided method for color matching or a computer color matching system (CCM system) which comprises computing the formulating amounts of one or a plurality of colorants and one or a plurality of effect materials like metallic or pearlescent pigments (briefly; metallic or pearlescent pigments) which are necessary for coloring a substrate surface to the same goniochromatism as a target color in the coating of a substrate with a coating composition containing metallic or pearlescent pigment (hereinafter a metallic or pearlescent coating composition) by a given application procedure for matching the metallic or pearlescent coating to the target color in goniochromatism. The metallic or pearlescent coating composition mentioned above means a coating composition containing one or a plurality of metallic and/or pearlescent pigments or said metallic pigments and/or pearlescent pigments plus one or a plurality of colorants.
In the color matching of a metallic or pearlescent coating composition, it is necessary to match it to a desired color sample (hereinafter referred to as sample color or target color) in goniochromatism. Goniochromatism is the term for the phenomenon whereby the color of a specimen depends on angular conditions of illumination and viewing and a special case of goniochromatism is the case in which the variation in appearance with angle is caused by a variation in the amount of light specularly reflected from the surface which appearance is called luster or briefly lightness flop. Goniochromatism that involves a variation of hue as well as lightness and saturation, thereby exhibiting a color variation with angle that is not perceived as luster, is called goniochromic or briefly hue or color flop. In certain cases, a coating composition must be formulated to reproduce the lightness flop and color flop of the target color according to a given coating thickness on a predetermined substrate using a predetermined coating procedure. In the color matching of a metallic or pearlescent coating composition, it is common practice to use a CCM system to compute the formulating amounts of colorants with respect to a metallic or pearlescent pigment component in a given formulating ratio. The commonly practiced CCM system employs prepared coated plates as base or reference data for evaluating the chromophoric activity of the colorant to be used for coloration of a substrate under a predetermined set of conditions, i.e. using a predetermined proportion of metallic or pearlescent pigment and a predetermined coating procedure. The commonly practiced CCM causes a computer to perform formulation computations using previously input spectral reflectance data of said coated plates.
In the conventional CCM system, the method in broad use comprises measuring the spectral reflectance of said target color, calculating the absorption coefficient and scattering coefficient in visible light from said spectral reflectance obtained from the colored plate as base data in accordance with the Kubelka-Munk optical density model for computing the predicted spectral reflectance of a given formulation of a plurality of colorants to be used for coloration and comparing the predicted spectral reflectance with the reflectance of the target color to find a colorant formulation conforming to the target color. In this comparison, if the difference between the target color and the predicted color exceeds a predetermined value, the colorant formulation is altered until it has come into a predetermined range and if the difference is found to be within the predetermined range, the result is used as the formulation value in actual formulation.
In the CCM of a metallic or pearlescent coating composition, the base data samples used are formulation samples comprising the respective chromatic colorants to be used and a metallic or pearlescent pigment for matching a target color. Using those data as reference data representing the chromaticity of the chromatic colorants with respect to the metallic or pearlescent pigment, the predicted reflectance that will be obtained on mixing a plurality of chromatic colorants with the metallic or pearlescent pigment is computed as follows. The spectral reflectances of the base data as measured beforehand are transformed to the optical density K/S, which is the ratio of the absorption coefficient K to the scattering coefficient S of the colored layer using the Kubelka-Munk equation and the optical density K/S is computed by the 2-constant method which is based on Duncan""s theoretical expression of color mixing. This K/S is further transformed to reflectance to compute the formulating ratio of the colorants to the metallic or pearlescent pigment.
To improve the prediction accuracy in the above procedure, a transformation to ideal reflectance is performed using Sanderson""s equation to correct for the influences of internal mirror reflection as well as the difference in refractive index at the boundary between the resin layer constituting the paint and the air layer on spectral reflectance measurement, then a color mixing computation is carried out. For matching a colorant formulation to the target color by adjusting the formulating ratio of the colorants, the computation according to the Newton-Raphson formula is repeated and for evaluating the chromaticity matching between the * target reflectance distribution and predicted reflectance distribution, the metameric method in which a convergence is sought by means of the Newton-Raphson formula while the difference between the target and predicted values is assessed by utilizing the chromaticity values. XYZ and L*a*b as calculated from reflectance, or the isomeric method in which a converging calculation is made while assessing the square sum of the difference between the target reflectance and the predicted reflectance.
Formulation of colorants matching a target color using this CCM system comprises a series of computations for finding the formulating values of said colorants under a specific set of conditions, such as a given coating thickness, a given substrate surface and other fixed conditions. On the other hand, the formulating amount of the metallic or pearlescent pigment for attaining the desired goniochromatism is determined by empirical judgment using the information available beforehand. Then, an actual coating composition is prepared according to the desired conditions and goniochromism of the target color sample so prepared is compared with that of the target color sample and, in addition, the luster of the color sample is compared with the desired luster. In the absence of sufficient agreement in goniochromism or in luster, the combination of colorants used for color matching and the kind and formulating amount of the metallic or pearlescent pigment are modified, and the CCM for correction is performed again, or the colorant formation and metallic or pearlescent pigment formulation that are not sufficiently matching are evaluated visually and empirically and adjusted against the empirical yardstick. This adjustment is repeated until sufficient matches have been obtained to the target hue and luster.
In the above prior art technology, the calculation means for finding the formulating values of the colorants and metallic or pearlescent pigment for realizing the desired goniochromatism has not been implemented in the CCM system and in order to arrive at a colorant and metallic or pearlescent pigment formulation giving a sufficient match to the desired hue and luster, the CCM must be repeated a plurality of times or the visual and empirical adjustment be made on a trial-and-error basis. This is because, in the matching to the desired hue and luster, the hue is not only influenced by the kinds of colorants but also by the formulating amount of the metallic or pearlescent pigment and the luster is influenced not only by the kind of metallic or pearlescent pigment but also by the colorant formulation and the coating thickness, thus necessitating it to compute the formulating ratio of the colorants to the metallic or pearlescent pigment taking such influences into account.
For the purpose of determining an adequate formulating ratio of colorants to metallic or pearlescent pigments or an adequate overall formulation, which will be faithful matching to the target color in both hue and luster, the conventional technology has to depend on many empirical judgments and it is extremely difficult even for a well experienced specialist to make accurate adjustments or perform a pertinent trial. Therefore, due to the relatively high number of trials and errors required to achieve the target colorant-metallic or pearlescent formulation, conventional color matching for coatings containing metallics and pearlescents requires much time and labor and is relatively expensive. Furthermore, since a critical color matching calls for much experience and cognitive expertise, there is no guarantee that the desired hue and luster can be obtained by conducting such trials.
In view of the above state of the art, the object of the present invention is to provide a method for computer-aided color matching that easily and accurately computes a formulating ratio of colorants to metallic or pearlescent pigments with the desired hue and luster characteristics of a metallic or pearlescent coating composition.
Developed to accomplish the above object, the present invention is a method of determining a formulating ratio of a colorant to a metallic or pearlescent pigment or a formulating amount of a metallic or pearlescen: pigment in a computer color matching of a coating composition containing a metallic or pearlescent pigment which comprises measuring the spectral reflectances of a plurality of coated plate specimens of varied formulating amount of the metallic or pearlescent pigment to be used or formulating ratio of the metallic or pearlescent pigment to be used to the colorant with a goniospectrophotometer, storing the resulting data in a memory of a computer in advance and executing an algorithm for predicting reproduction gonio-spectral reflectances while inputting changes in gonio-spectral reflectances as caused by varying the level of addition of the metallic or pearlescent pigment using said stored data to find an adequate formulating amount of said metallic or pearlescent pigment or an adequate formulating ratio of said metallic or pearlescent pigment to the colorant.
The method of the present invention is further characterized in that, while determining the formulating ratio of the metallic or pearlescent pigment to the colorant or the formulating amount of the metallic or pearlescent pigment in the computer color matching of the coating composition containing the metallic or pearlescent pigment, the predictive reproduction gonio-gonio-spectral reflectances is subjected to correction procedure comprising the steps of
i) generating the gonio-spectral reflectance data of a coating comprising one or more metallic or pearlescent pigments or one or more metallic or pearlescent pigments and one or more colorants inclusive of a translucent pigment and the formulating amount or ratio data thereof or said two kinds of data and coating thickness data for taking into account the influence of under coating color or substrate color and coating thickness as measured for one or a plurality of coated plate samples,
ii) storing said data in a memory of the computer in advance and
iii) correcting for the difference between the stored data and the gonio-spectral reflectance predicted by the computerhm over the entire measuring wavelength range and entire angular range by a fuzzy logic (same as; a fuzzy deduction algorithm) to thereby improve the accuracy of color matching.
The method of the present invention thus preferably is that, for determining the formulating ratio of the metallic or pearlescent pigment to the colorant or the formulating amount of the metallic or pearlescent pigment in a computer-aided color matching of a coating composition containing one or more colorants and one or more metallic or pearlescent pigments as the target color for reproduction, the color matching comprises measuring the spectral reflectances of the colorants and metallic or pearlescent pigments of said target color with a goniospectrophotometer, predicting gonio-spectral reflectances taking into account the changes in spectral reflectance which occur depending on the illumination angle and receiving light angle which is characterize of a metallic-pearlescent coating, and determining an adequate formulating ratio of the metallic or pearlescent pigment to the colorant or the formulating amount of the metallic or pearlescent pigment using the steps consisting of:
(a) performing a predictive computation of reproduction gonio-spectral reflectances from the previously measured gonio-spectral reflectance data of the colorant and metallic or pearlescent pigment,
(b) computing the optical densities suitable for a metallic or pearlescent coating which are necessary for the prediction of reproduction gonio-spectral reflectances,
(c) performing a color matching computation to determine the formulating ratio of the metallic or pearlescent pigment to the colorant or the formulating amount of the metallic or pearlescent pigment, and
(d) storing the gonio-spectral reflectance, formulating ratio, formulating amount and coating condition data of a coating prepared beforehand for use as a reference in a memory of the computer and executing a fuzzy deduction algorithm to correct for the difference between reproduction gonio-spectral reflection data and said reference gonio-spectral reflection data over the entire measuring wavelength range and entire angular range.